Hybrid Approach of Radial Basis Function and Finite Element Method for Electromagnetic Problems

This paper presents a novel approach for the analysis of electromagnetic problems, namely radial basis function (RBF) mixed with Galerkin finite element method (FEM). The new method divides computational domain into a series of sub-domains and uses the point interpolation based on RBF to obtain the shape functions, respectively. Then, each separate domain is taken as elements of the Galerkin FEM to approximate the solutions of the entire computational area. Using this method, the coefficient matrix becomes sparse; and strict meshing is not necessary. The hybrid method also combines the advantages of RBF and FEM, such as easy to handle complex boundary conditions for FEM and high efficient fitting for RBF. Two electromagnetic problems are computed to verify the method. Meanwhile, two traditional methods are also investigated to prove the advantages of the proposed method as a comparison.